I am currently working under the mentorship of Dr. David P. Herzog. We study the asymptotic stability of nonlinear stochastic dynamics. Our most recent pre-print establishes explicit rates of convergence for Langevin dynamics subject to singular potentials in a weighted norm. More recently, we are focusing on the asymptotic behavior of degenerately stochastically forced Lorenz 96 systems.
My mathematical research and interests lie in:
Chaos Theory and Nonlinear Dynamics
Partial Differential Equations
A recent presentation of our Langevin dynamics results.
Research with Undergraduates
I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:
Fractals and iterated function systems
Sampling and interpolation theory
Markov chains and mixing times
Models for turbulent flow
Fractional operator theory